Theorem 2.18 - Fundamental Logical Equivalences

1. • \((P \vee Q) \iff (Q \vee P)\)
   • \((P \wedge Q) \iff (Q \wedge P)\)
2. • \(P \vee (Q \vee R) \iff (P \vee Q) \vee R\)
   • \(P \wedge (Q \wedge R) \iff (P \wedge Q) \wedge R\)
3. • \(P \vee (Q \wedge R) \iff (P \vee Q) \wedge (P \vee R)\)
   • \(P \wedge (Q \vee R) \iff (P \wedge Q) \vee (P \wedge R)\)
4. • \(\neg{(P \vee Q)} \iff (\neg{P}) \wedge (\neg{Q})\)
   • \(\neg{(P \wedge Q)} \iff (\neg{P}) \vee (\neg{Q})\)

Example: Write negations of the following open sentences:

• internet was unstable during lecture, couldn't get these copied down. should be in recording from September 1st!